Pith Number

pith:YT57W6QP

pith:2011:YT57W6QPSRSRVCXMIJ6GCIQ4PF

not attested not anchored not stored refs pending

Two isoperimetric inequalities for the Sobolev constant

Jesse Ratzkin, Tom Carroll

arxiv:1105.2719 v1 · 2011-05-13 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YT57W6QPSRSRVCXMIJ6GCIQ4PF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:21:39.901650Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4fbfb7a0f94651a8aec427c61221c7979092be53a9a07309c301afe130dfa14

Aliases

arxiv: 1105.2719 · arxiv_version: 1105.2719v1 · doi: 10.48550/arxiv.1105.2719 · pith_short_12: YT57W6QPSRSR · pith_short_16: YT57W6QPSRSRVCXM · pith_short_8: YT57W6QP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YT57W6QPSRSRVCXMIJ6GCIQ4PF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c4fbfb7a0f94651a8aec427c61221c7979092be53a9a07309c301afe130dfa14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5247049cd1cc693fe38b1c3c4753e35effb7c3b8ff74e77d92e859ffa68c2766",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-05-13T13:17:48Z",
    "title_canon_sha256": "824de862db724aebb92ede26d876e6fd084bf61f192911740ed0c122568a29a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2719",
    "kind": "arxiv",
    "version": 1
  }
}